Optimal LQG Control Across a Packet-Dropping Link

We examine optimal Linear Quadratic Gaussian control for a system in which communication between the sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend the familiar LQG separation principle to this problem that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. We present one such optimal algorithm, which consists of a Kalman Filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design

Optimization flow control with estimation error

We analyze the effects of price estimation error in a dual-gradient optimization flow control scheme, and characterize the performance of the algorithm in this case. By treating estimation error as inexactness of the gradient, we utilize sufficient conditions for convergence subject to bounded error to characterize the long-term dynamics of the link utilization in terms of a region, which the trajectory enters in finite time. We explicitly find bounds for this region under a particular quantization error model, and provide simulation results to verify the predicted behavior of the system. Finally, we analyze the effects of the stepsize on the convergence of the algorithm, and provide analytical and numerical results, which suggest a particular choice for this parameter

Asynchronous Distributed Averaging on Communication Networks

Distributed algorithms for averaging have attracted interest in the control and sensing literature. However, previous works have not addressed some practical concerns that will arise in actual implementations on packet-switched communication networks such as the Internet. In this paper, we present several implementable algorithms that are robust to asynchronism and dynamic topology changes. The algorithms are completely distributed and do not require any global coordination. In addition, they can be proven to converge under very general asynchronous timing assumptions. Our results are verified by both simulation and experiments on Planetlab, a real-world TCP/IP network. We also present some extensions that are likely to be useful in applications

Effects of reproductive and demographic changes on breast cancer incidence in China: A modeling analysis

Background: Breast cancer incidence is currently low in China. However, the distribution of reproductive and lifestyle risk factors for breast cancer among Chinese women is changing rapidly. We quantified the expected effect of changes in breast cancer risk factors on future rates of breast cancer in China. Methods: We first validated and calibrated the Rosner-Colditz log-incidence breast cancer model in Chinese women who participated in the Shanghai Women's Health Study cohort (N = 74 942). We then applied the calibrated model to a representative sample of Chinese women who were aged 35-49 years in 2001 using data from the Chinese National Family Planning and Reproductive Health Survey (NFPRHS, N = 17 078) to predict the age-specific and cumulative breast cancer incidence among all Chinese women of this age group. We evaluated the relative impact of changes in modifiable risk factors, including alcohol intake, parity, postmenopausal hormone use, and adult weight gain, on cumulative incidence of breast cancer. Results: Breast cancer incidence in China is expected to increase substantially from current rates, estimated at 10-60 cases per 100 000 women, to more than 100 new cases per 100 000 women aged 55-69 years by 2021. We predicted 2.5 million cases of breast cancer by 2021 among Chinese women who were 35-49 years old in 2001. Modest reductions in hormone and alcohol use, and weight maintenance could prevent 270 000 of these cases. Conclusions: China is on the cusp of a breast cancer epidemic. Although some risk factors associated with economic development are largely unavoidable, the substantial predicted increase in new cases of breast cancer calls for urgent incorporation of this disease in future health care infrastructure planning

Optimal LQG control across packet-dropping links

Abstract We examine two special cases of the problem of optimal Linear Quadratic Gaussian control of a system whose state is being measured by sensors that communicate with the controller over packet-dropping links. We extend the LQG separation principle using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. Our design is optimal for any arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design

Approximate distributed Kalman filtering in sensor networks with quantifiable performance

We analyze the performance of an approximate distributed Kalman filter proposed in recent work on distributed coordination. This approach to distributed estimation is novel in that it admits a systematic analysis of its performance as various network quantities such as connection density, topology, and bandwidth are varied. Our main contribution is a frequency-domain characterization of the distributed estimator's steady-state performance; this is quantified in terms of a special matrix associated with the connection topology called the graph Laplacian, and also the rate of message exchange between immediate neighbors in the communication network

Distributed Gradient Systems and Dynamic Coordination

Many systems comprised of interconnected sub-units exhibit coordinated behaviors; social groups, networked computers, financial markets, and numerous biological systems come to mind. There has been long-standing interest in developing a scientific understanding of coordination, both for explanatory power in the natural and economic sciences, and also for constructive power in engineering and applied sciences. This thesis is an abstract study of coordination, focused on developing a systematic "design theory" for producing interconnected systems with specifiable coordinated behavior; this is in contrast to the bulk of previous work on this subject, in which any design component has been primarily ad-hoc. The main theoretical contribution of this work is a geometric formalism in which to cast distributed systems. This has numerous advantages and "naturally" parametrizes a wide class of distributed interaction mechanisms in a uniform way. We make use of this framework to present a model for distributed optimization, and we introduce the distributed gradient as a general design tool for synthesizing dynamics for distributed systems. The distributed optimization model is a useful abstraction in its own right and motivates a definition for a distributed extremum. As one might expect, the distributed gradient is zero at a distributed extremum, and the dynamics of a distributed gradient flow must converge to a distributed extremum. This forms the basis for a wide variety of designs, and we are in fact able to recover a widely studied distributed averaging algorithm as a very special case. We also make use of our geometric model to introduce the notion of coordination capacity; intuitively, this is an upper bound on the "complexity" of coordination that is feasible given a particular distributed interaction structure. This gives intuitive results for local, distributed, and global control architectures, and allows formal statements to be made regarding the possibility of "solving" certain optimization problems under a particular distributed interaction model. Finally, we present a number of applications to illustrate the theoretical approach presented; these range from "standard" distributed systems tasks (leader election and clock synchronization) to more exotic tasks like graph coloring, distributed account balancing, and distributed statistical computations.</p

Distributed Gradient Systems and Dynamic Coordination

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Optimization Flow Control with Estimation Error

We analyze the effects of price estimation error in a dual-gradient optimization flow control scheme, and characterize the performance of the algorithm in this case. By treating estimation error as inexactness of the gradient, we utilize sufficient conditions for convergence subject to bounded error to characterize the long-term dynamics of the link utilization in terms of a region which the trajectory enters in finite time. We explicitly find bounds for this region under a particular quantization error model, and provide simulation results to verify the predicted behavior of the system. Finally, we analyze the effects of the stepsize on the convergence of the algorithm, and provide analytical and numerical results which suggest a particular choice for this parameter